Levy's zero-one law in game-theoretic probability

Glenn Shafer, Vladimir Vovk, Akimichi Takemura

Research output: Working paper

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We prove a game-theoretic version of Levy's zero-one law, and deduce several corollaries from it, including non-stochastic versions of Kolmogorov's zero-one law, the ergodicity of Bernoulli shifts, and a zero-one law for dependent trials. Our secondary goal is to explore the basic definitions of game-theoretic probability theory, with Levy's zero-one law serving a useful role.
Original languageEnglish
Publication statusPublished - 3 May 2009


  • math.PR
  • 60F20

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